Normal hydraulic fracturing treatment design calculations combine fracture mechanics, fluid mechanics, and a volume balance to predict fracture growth with time. Fracture mechanics relates fracture width to pressure and fracture length, height, or radius; fluid mechanics relates pressure to injection rate, width, and length or radius; and the volume balance relates the fracture volume to injection and fluid-loss rates.
Shlypaborsky, et al. in Society of Petroleum Engineers (SPE) Paper Nos. 18194 and 18195 noted that pressures obtained during fracturing treatments do not always agree with pressures predicted by fracture design models. Shlypaborsky listed five factors that have the potential for causing this disagreement: (1) high perforation friction pressure, (2) high friction pressure in the fracture, (3) the generation of multiple parallel fractures, (4) higher actual fracture toughness values than measured in the lab, and (5) a non-penetrating region near the fracture tip. To isolate the cause of the disagreement, Shlypaborsky et al. measured overpressure, which is the difference between downhole instantaneous shut-in pressure and the least principle stress, and thus eliminated the three friction-related effects from consideration. The overpressure, the result of one or both of the remaining two factors, was then used to determine an apparent fracture toughness. The apparent fracture toughness was subsequently used in a geometry model that considered fracture toughness in its solution to the fracture mechanics portion of the problem.
The methods of the present invention overcome many of the deficiencies in prior methods for determining fracture geometry. The new methods are further described in CIM/SPE paper 90-42 which is incorporated by reference.
To compensate for all four of the factors that may occur within the fracture and to provide more flexibility, methods in accordance with the present invention were developed that substitute net pressure for fluid mechanics determinations. The term "net pressure" as used herein refers to the difference between bottomhole treating pressure and least principle stress. By substituting (1) a given net (excess) pressure value, (2) a correlation between net pressure and time, or (3) a set of net pressure values for the net pressures determined through fluid mechanics relationships, methods that can determine fracture geometry for use in fracturing treatment design, monitoring, and analysis have been developed. The methods of the present invention allow calculations to be made for fracture design models which are well known to those skilled in the art, such as radial (penny-shaped) fracture geometry and geometries based on Khristianovic-Zheltov and Perkins and Kern width equations for constant height fractures. By considering the variation of injection rate and pressure with time, the method can also be used to calculate fracture behavior during shut-in and flowback as well as during injection.
The methods of the present invention also take into account situations such as multiple parallel fractures, faults, and natural fractures. In addition, by considering fluid mechanics, the limits set on the exponent relating pressure to time are expanded to radial models and models using the Khristianovic-Zheltov width equation as well as models using the Perkins and Kern width equation.